Group #15765513 — subgroups

Subgroups — #15765513

Order 3328.

626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718748	C₂	1	2	yes	maximal
2	#13115630	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718139	C₂	1	2	yes	maximal, complemented
4	#13112671	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×Q₁₆	—	2	2	no	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
9	C₁₃×#494	—	2	4	no	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88060	—	2	2	no	—
12	#11718748	—	2	4	no	—
13	#11718748	—	2	4	no	—
14	C₂×#88049	—	2	2	no	—
15	C₂×#88047	—	2	2	no	—
16	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#1055	C₂²	1	2	yes	—
18	#11718139	—	2	4	no	—
19	C₂²×Q₈×C₁₃	—	2	2	no	—
20	C₂²×D₅₂	D₄	1	1	yes	characteristic
21	C₂²×C₄×D₁₃	—	2	1	no	—
22	C₂×C₁₃×Q₁₆	—	2	8	no	—
23	C₂×C₁₃×Q₁₆	—	4	4	no	—
24	C₂×C₁₃×Q₁₆	—	4	4	no	—
25	C₂²×C₈×C₁₃	D₄	1	2	yes	—
26	C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₁₃×C₄⋊Q₈	—	2	2	no	—
28	C₁₃×C₄⋊Q₈	—	2	2	no	—
29	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
33	C₂×#6103	—	2	1	no	—
34	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
35	C₂²×#1055	—	2	2	no	—
36	C₂²×#1055	—	2	1	no	—
37	C₄×D₅₂	—	2	2	no	—
38	C₄×D₅₂	—	2	2	no	—
39	C₄×C₈×C₁₃	—	2	2	no	—
40	#88060	—	4	4	no	—
41	#88049	—	2	8	no	—
42	#88047	—	2	8	no	—
43	C₄⋊#1055	—	2	2	no	—
44	C₄⋊#1055	—	2	2	no	—
45	C₄⋊#1055	D₄	1	4	yes	—
46	#10274	—	13	1	no	maximal, Sylow
47	C₂³×D₁₃	—	2	1	no	—
48	C₂×Q₈×C₁₃	—	2	4	no	—
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂×Q₈×C₁₃	—	4	4	no	—
51	C₂×Q₈×C₁₃	—	4	4	no	—
52	C₂²×C₄×C₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
56	C₂²×Dic₁₃	—	2	1	no	—
57	C₂×D₅₂	—	2	2	no	—
58	C₂×D₅₂	—	2	2	no	—
59	C₂×D₅₂	—	2	1	no	—
60	C₂×D₅₂	Q₁₆	1	2	yes	complemented
61	C₂×C₄×D₁₃	—	4	1	no	—
62	C₂×C₄×D₁₃	—	4	1	no	—
63	C₂×C₄×D₁₃	—	4	2	no	—
64	C₂×C₄×D₁₃	—	4	2	no	—
65	C₁₃×Q₁₆	—	4	16	no	—
66	C₂×C₈×C₁₃	—	2	2	no	—
67	C₂×C₈×C₁₃	—	2	2	no	—
68	C₂×C₈×C₁₃	D₈	1	4	yes	—
69	C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₄²×C₁₃	C₂×D₄	1	2	yes	—
74	C₄²×C₁₃	C₂×D₄	1	2	yes	—
75	#6103	—	4	2	no	—
76	C₄⋊Dic₁₃	—	2	2	no	—
77	C₂×#1055	—	2	4	no	—
78	C₂×#1055	—	4	2	no	—
79	C₂×#1055	—	4	2	no	—
80	C₂×#1055	—	4	1	no	—
81	C₂×#1055	—	4	2	no	—
82	C₂×#494	D₁₃	1	1	yes	characteristic, complemented
83	C₂×#474	—	13	2	no	—
84	#1954	—	13	1	no	—
85	C₂×#332	—	13	2	no	—
86	#1277	—	13	1	no	—
87	C₂³×C₁₃	#121	1	1	yes	characteristic
88	C₂²×D₁₃	—	2	2	no	—
89	C₂²×D₁₃	—	4	1	no	—
90	C₂²×D₁₃	—	4	2	no	—
91	C₂²×D₁₃	—	4	1	no	—
92	C₂²×D₁₃	—	4	2	no	—
93	Q₈×C₁₃	—	4	8	no	—
94	Q₈×C₁₃	—	8	2	no	—
95	Q₈×C₁₃	—	8	2	no	—
96	C₂×C₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	4	4	no	—
98	C₂×C₄×C₁₃	—	8	4	no	—
99	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#120	1	2	yes	—
101	C₂×C₄×C₁₃	#121	1	2	yes	—
102	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
104	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
106	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
107	C₂×C₄×C₁₃	#137	1	2	yes	—
108	C₂×Dic₁₃	—	4	1	no	—
109	C₂×Dic₁₃	—	4	2	no	—
110	D₅₂	—	2	4	no	—
111	D₅₂	—	4	2	no	—
112	C₄×D₁₃	—	8	2	no	—
113	C₄×D₁₃	—	8	1	no	—
114	C₄×D₁₃	—	8	1	no	—
115	C₈×C₁₃	—	2	4	no	—
116	#1055	—	4	4	no	—
117	#1055	—	8	1	no	—
118	C₂²×Q₁₆	—	2	2	no	—
119	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
120	C₂×C₄×D₄	—	13	1	no	—
121	#494	—	2	4	no	—
122	#474	—	26	4	no	—
123	#474	—	26	4	no	—
124	C₂×#107	—	26	2	no	—
125	C₂×C₄⋊C₈	—	13	2	no	—
126	C₂×C₄⋊C₈	—	13	1	no	—
127	C₂×#102	—	26	2	no	—
128	C₂×C₂²⋊C₈	—	26	2	no	—
129	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
130	#332	—	26	4	no	—
131	C₂²×C₁₃	#392	1	1	yes	characteristic
132	C₂²×C₁₃	#459	1	2	yes	—
133	C₂²×C₁₃	#467	1	1	yes	characteristic
134	C₂²×C₁₃	#470	1	1	yes	characteristic
135	C₂²×C₁₃	#473	1	2	yes	—
136	C₂×D₁₃	—	4	4	no	—
137	C₂×D₁₃	—	4	2	no	—
138	C₂×D₁₃	—	8	2	no	—
139	C₂×D₁₃	—	8	1	no	—
140	C₂×D₁₃	—	8	1	no	—
141	C₄×C₁₃	—	2	2	no	—
142	C₄×C₁₃	—	8	4	no	—
143	C₄×C₁₃	#447	1	2	yes	—
144	C₄×C₁₃	#451	1	2	yes	—
145	C₄×C₁₃	#452	1	2	yes	—
146	C₄×C₁₃	#493	1	1	yes	characteristic
147	C₄×C₁₃	#496	1	1	yes	characteristic
148	Dic₁₃	—	8	1	no	—
149	C₂²×Q₈	—	2	2	no	—
150	C₂²×D₄	—	13	1	no	—
151	C₂³×C₄	—	26	1	no	—
152	C₂×Q₁₆	—	2	8	no	—
153	C₂×Q₁₆	—	4	4	no	—
154	C₂×Q₁₆	—	4	4	no	—
155	C₂²×C₈	—	26	2	no	—
156	C₂²×C₈	—	26	1	no	—
157	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	C₂²⋊D₁₃	1	4	yes	—
162	C₄×D₄	—	26	2	no	—
163	C₄×D₄	—	26	2	no	—
164	C₂×C₄⋊C₄	—	2	2	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	13	1	no	—
167	C₂×C₂²⋊C₄	—	26	1	no	—
168	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
169	#107	—	26	8	no	—
170	C₄⋊C₈	—	13	4	no	—
171	C₄⋊C₈	—	26	2	no	—
172	C₄⋊C₈	—	26	2	no	—
173	#102	—	26	8	no	—
174	C₂²⋊C₈	—	52	4	no	—
175	C₄×C₈	—	2	2	no	—
176	C₂×C₁₃	#1669	1	2	yes	—
177	C₂×C₁₃	#1689	1	2	yes	—
178	C₂×C₁₃	#2001	1	1	yes	characteristic
179	C₂×C₁₃	#2011	1	1	yes	characteristic
180	C₂×C₁₃	#2020	1	1	yes	characteristic
181	D₁₃	—	8	2	no	—
182	C₂⁴	—	26	1	no	—
183	C₂×Q₈	—	2	4	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂×Q₈	—	4	4	no	—
186	C₂×Q₈	—	4	4	no	—
187	C₂×D₄	—	13	2	no	—
188	C₂×D₄	—	26	2	no	—
189	C₂×D₄	—	26	1	no	—
190	C₂×D₄	—	26	2	no	—
191	C₂²×C₄	—	4	2	no	—
192	C₂²×C₄	—	26	1	no	—
193	C₂²×C₄	—	52	2	no	—
194	C₂²×C₄	—	52	2	no	—
195	C₂²×C₄	—	52	1	no	—
196	C₂²×C₄	—	52	1	no	—
197	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
198	C₂²×C₄	#6129	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
200	Q₁₆	—	4	16	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	26	4	no	—
204	C₂×C₈	—	52	2	no	—
205	C₂×C₈	—	52	2	no	—
206	C₂×C₈	—	52	2	no	—
207	C₂×C₈	—	52	1	no	—
208	C₂×C₈	#6104	1	4	yes	—
209	C₄⋊C₄	—	2	4	no	—
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	—	4	2	no	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄⋊C₄	—	26	2	no	—
214	C₂²⋊C₄	—	52	2	no	—
215	C₄²	D₄×D₁₃	1	2	yes	—
216	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
217	C₁₃	#10274	1	1	yes	characteristic, complemented, Sylow
218	C₂³	—	26	2	no	—
219	C₂³	—	52	2	no	—
220	C₂³	—	52	1	no	—
221	C₂³	—	52	2	no	—
222	C₂³	—	52	1	no	—
223	C₂³	#88192	1	1	yes	characteristic
224	Q₈	—	4	8	no	—
225	Q₈	—	8	2	no	—
226	Q₈	—	8	2	no	—
227	D₄	—	26	4	no	—
228	D₄	—	52	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	4	4	no	—
231	C₂×C₄	—	8	4	no	—
232	C₂×C₄	—	52	2	no	—
233	C₂×C₄	—	52	1	no	—
234	C₂×C₄	—	104	1	no	—
235	C₂×C₄	—	104	1	no	—
236	C₂×C₄	—	104	2	no	—
237	C₂×C₄	Q₁₆×D₁₃	1	1	yes	characteristic
238	C₂×C₄	#88172	1	2	yes	—
239	C₂×C₄	#88173	1	1	yes	characteristic
240	C₂×C₄	C₂×#6104	1	2	yes	—
241	C₂×C₄	#88186	1	2	yes	—
242	C₂×C₄	#88191	1	2	yes	—
243	C₂×C₄	#88193	1	2	yes	—
244	C₂×C₄	#88194	1	1	yes	characteristic
245	C₂×C₄	#88207	1	1	yes	characteristic
246	C₈	—	2	4	no	—
247	C₈	—	52	4	no	—
248	C₈	—	104	1	no	—
249	C₂²	—	52	4	no	—
250	C₂²	—	52	2	no	—
251	C₂²	—	104	1	no	—
252	C₂²	—	104	1	no	—
253	C₂²	—	104	2	no	—
254	C₂²	#11718733	1	2	yes	—
255	C₂²	#11718849	1	1	yes	characteristic
256	C₂²	#11718850	1	1	yes	characteristic
257	C₂²	#11718853	1	2	yes	—
258	C₂²	#11718884	1	1	yes	characteristic
259	C₄	—	2	2	no	—
260	C₄	—	8	4	no	—
261	C₄	—	104	1	no	—
262	C₄	#11718734	1	1	yes	characteristic
263	C₄	#11718735	1	1	yes	characteristic
264	C₄	#11718847	1	2	yes	—
265	C₄	#11718848	1	2	yes	—
266	C₄	#11718878	1	2	yes	—
267	C₂	—	104	2	no	—
268	C₂	#13114198	1	2	yes	—
269	C₂	#13114322	1	2	yes	—
270	C₂	#13115843	1	1	yes	characteristic
271	C₂	#13115907	1	1	yes	characteristic
272	C₂	#13115955	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718748

C₂

yes

maximal

#13115630

C₂

yes

maximal, characteristic

C₂×#11718139

C₂

yes

maximal, complemented

#13112671

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×#494

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₃×Q₁₆

—

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

—

C₂×C₄×D₅₂

C₂²

yes

characteristic

C₁₃×#494

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

—

—

—

—

C₂×C₄⋊#1055

C₂²

yes

characteristic

C₂×C₄⋊#1055

C₂²

yes

—

#11718139

—

C₂²×Q₈×C₁₃

—

C₂²×D₅₂

D₄

yes

characteristic

C₂²×C₄×D₁₃

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₂²×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×#6103

—

C₂×C₄⋊Dic₁₃

D₄

yes

characteristic

C₂²×#1055

—

C₂²×#1055

—

C₄×D₅₂

—

C₄×D₅₂

—

C₄×C₈×C₁₃

—

—

—

—

—

—

D₄

yes

—

#10274

—

maximal, Sylow

C₂³×D₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

characteristic

C₂²×Dic₁₃

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

Q₁₆

yes

complemented

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₈

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

C₂×D₄

yes

—

#6103

—

C₄⋊Dic₁₃

—

—

—

—

—

—

D₁₃

yes

characteristic, complemented

—

—

—

—

C₂³×C₁₃

#121

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

characteristic

100

C₂×C₄×C₁₃

#120

yes

—

101

C₂×C₄×C₁₃

#121

yes

—

102

C₂×C₄×C₁₃

#127

yes

characteristic

103

C₂×C₄×C₁₃

C₂×D₈

yes

—

104

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

105

C₂×C₄×C₁₃

#135

yes

characteristic

106

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

107

C₂×C₄×C₁₃

#137

yes

—

108

C₂×Dic₁₃

—

109

C₂×Dic₁₃

—

110

D₅₂

—

111

D₅₂

—

112

C₄×D₁₃

—

113

C₄×D₁₃

—

114

C₄×D₁₃

—

115

C₈×C₁₃

—

116

#1055

—

117

#1055

—

118

C₂²×Q₁₆

—

119

C₂×C₄⋊Q₈

C₂×D₁₃

yes

—

120

C₂×C₄×D₄

—

121

#494

—

122

#474

—

123

#474

—

124

C₂×#107

—

125

C₂×C₄⋊C₈

—

126

C₂×C₄⋊C₈

—

127

C₂×#102

—

128

C₂×C₂²⋊C₈

—

129

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

130

#332

—

131

C₂²×C₁₃

#392

yes

characteristic

132

C₂²×C₁₃

#459

yes

—

133

C₂²×C₁₃

#467

yes

characteristic

134

C₂²×C₁₃

#470

yes

characteristic

135

C₂²×C₁₃

#473

yes

—

136

C₂×D₁₃

—

137

C₂×D₁₃

—

138

C₂×D₁₃

—

139

C₂×D₁₃

—

140

C₂×D₁₃

—

141

C₄×C₁₃

—

142

C₄×C₁₃

—

143

C₄×C₁₃

#447

yes

—

144

C₄×C₁₃

#451

yes

—

145

C₄×C₁₃

#452

yes

—

146

C₄×C₁₃

#493

yes

characteristic

147

C₄×C₁₃

#496

yes

characteristic

148

Dic₁₃

—

149

C₂²×Q₈

—

150

C₂²×D₄

—

151

C₂³×C₄

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

C₂²⋊D₁₃

yes

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

C₂²⋊D₁₃

yes

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₄²

C₂²×D₁₃

yes

characteristic

169

#107

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

#102

—

174

C₂²⋊C₈

—

175

C₄×C₈

—

176

C₂×C₁₃

#1669

yes

—

177

C₂×C₁₃

#1689

yes

—

178

C₂×C₁₃

#2001

yes

characteristic

179

C₂×C₁₃

#2011

yes

characteristic

180

C₂×C₁₃

#2020

yes

characteristic

181

D₁₃

—

182

C₂⁴

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

D₄×D₁₃

yes

characteristic

198

C₂²×C₄

#6129

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

200

Q₁₆

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

#6104

yes

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₂²⋊C₄

—

215

C₄²

D₄×D₁₃

yes

—

216

C₄²

C₂×C₂²⋊D₁₃

yes

—

217

C₁₃

#10274

yes

characteristic, complemented, Sylow

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

#88192

yes

characteristic

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

D₄

—

228

D₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

104

—

235

C₂×C₄

—

104

—

236

C₂×C₄

—

104

—

237

C₂×C₄

Q₁₆×D₁₃

yes

characteristic

238

C₂×C₄

#88172

yes

—

239

C₂×C₄

#88173

yes

characteristic

240

C₂×C₄

C₂×#6104

yes

—

241

C₂×C₄

#88186

yes

—

242

C₂×C₄

#88191

yes

—

243

C₂×C₄

#88193

yes

—

244

C₂×C₄

#88194

yes

characteristic

245

C₂×C₄

#88207

yes

characteristic

246

C₈

—

247

C₈

—

248

C₈

—

104

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

104

—

252

C₂²

—

104

—

253

C₂²

—

104

—

254

C₂²

#11718733

yes

—

255

C₂²

#11718849

yes

characteristic

256

C₂²

#11718850

yes

characteristic

257

C₂²

#11718853

yes

—

258

C₂²

#11718884

yes

characteristic

259

C₄

—

260

C₄

—

261

C₄

—

104

—

262

C₄

#11718734

yes

characteristic

263

C₄

#11718735

yes

characteristic

264

C₄

#11718847

yes

—

265

C₄

#11718848

yes

—

266

C₄

#11718878

yes

—

267

C₂

—

104

—

268

C₂

#13114198

yes

—

269

C₂

#13114322

yes

—

270

C₂

#13115843

yes

characteristic

271

C₂

#13115907

yes

characteristic

272

C₂

#13115955

yes

characteristic

	subgroup	G/H
center	C₂³	#88192
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#494	C₂
socle	C₂³×C₁₃	#121
prime radical	C₂²×D₅₂	D₄
hypercenter	C₂×#494	D₁₃
hypocenter	C₁₃	#10274
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#88192

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₂×C₁₃×#494

C₂

socle

C₂³×C₁₃

#121

prime radical

C₂²×D₅₂

D₄

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
3. C₂×#11718139	C₂	semidirect
4. #13112671	C₂	semidirect
5. C₂×C₁₃×#494	C₂	semidirect
60. C₂×D₅₂	Q₁₆	semidirect
82. C₂×#494	D₁₃	semidirect
217. C₁₃	#10274	semidirect

H ≅ G/N

type

3. C₂×#11718139

C₂

semidirect

4. #13112671

C₂

semidirect

5. C₂×C₁₃×#494

C₂

semidirect

60. C₂×D₅₂

Q₁₆

semidirect

82. C₂×#494

D₁₃

semidirect

217. C₁₃

#10274

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11718748	2
#13115630	2
C₂×#11718139	2
#13112671	2
C₂×C₁₃×#494	2
#10274	13

subgroup

index

C₂×C₁₃×#494

Subgroups — #15765513

Conjugacy classes of subgroups

Complements

Maximal subgroups